Question

A rocket is divided into three sections: the payload and navigation section in the top, the fuel section in the middle, and the rocket engine section in the bottom. The top section is one-sixth the length of the bottom section. The middle section is one-half the length of the bottom section. The total length is 240ft. Find the length of each section.

Answer 1

Let's name each of the three sections of the rocket as:

-
`P` payload and navigation

-
`F` fuel

-
`E` engine

Now, we are told that:

The top section is one-sixth the length of the bottom section:

`P=(1)/(6)E` (1)

The middle section is one-half the length of the bottom section:

`F=(1)/(2)E` (2)

The total length is 240ft:

`P+F+E=240ft` (3)

We may begin by substiting (1) and (2) in equation (3), in order to find the value of the engine section
`E`:

`(1)/(6)E+(1)/(2)E+E=240ft`

`E=144ft` (4)>>>> Value of the engine section length

Then, we substitute this value of
`E` in equations (1) and (2):

`P=(1)/(6)144ft`

`P=24ft` (5)>>>> Value of the payload and navigation section length

`F=(1)/(2)144ft`

`F=72ft` (6)>>>> Value of the fuel section length